Please show all work and answer all parts ### Analysis of Rocket ExplosionA small unpiloted test rocket is moving through space with a constant speed of 100 m/s. The total mass of the rocket is 1000 kg.#### Explosion DescriptionThe rocket explodes into three sections: A, B, and C (not shown in the diagram).- **Piece A:** - Mass: 600 kg - Speed: 60 m/s - Angle (\(\theta_A\)): 22° with respect to piece B's direction (not the horizontal).- **Piece B:** - Mass: 300 kg - Speed: 20 m/s - Angle (\(\theta_B\)): 15° with respect to the horizontal.#### Diagram ExplanationThe diagram shows:- Two fragments labeled A and B with vectors indicating their respective direction and angles.- An angle \(\theta_A\) representing the deviation of Piece A's direction from the trajectory of Piece B.- An angle \(\theta_B\) representing the angular deviation of Piece B's direction from the horizontal axis.#### TaskTo assist the research team in identifying the missing piece (Piece C), derive the expression for the momentum of Piece C in vector form based on the conservation of momentum principle. The total initial momentum should equal the total final momentum of all fragments.This serves as a practical application of physics concepts involving momentum conservation in isolated systems without external forces.

Given, Mass of rocket =1000 kg initial speed of rocket =100 m/s mass of piece A = 600 kg mass of…

A small unpiloted test rocket is moving through space (to the right in the picture) with a constant speed of 100 m/s. The total mass of the rocket is 1000kg. Suddenly the rocket explodes into three sections A, B and C (not shown) as depicted below. Piece A is 600 kg and is moving with a speed of 60 m/s, with 0A = 22° (note the way that angle is drawn in the picture. That is measured with respect to B, not the horizontal) Piece B is 300 kg and is moving with a speed of 20 m/s, with 0B = 15º with respect to the horizontal А 'B So that the research team can search for the missing piece (piece C), please write the expression for the momentum of that piece in vector form.

A small unpiloted test rocket is moving through space (to the right in the picture) with a constant speed of 100 m/s. The total mass of the rocket is 1000kg. Suddenly the rocket explodes into three sections A, B and C (not shown) as depicted below. Piece A is 600 kg and is moving with a speed of 60 m/s, with 0A = 22° (note the way that angle is drawn in the picture. That is measured with respect to B, not the horizontal) Piece B is 300 kg and is moving with a speed of 20 m/s, with 0B = 15º with respect to the horizontal А 'B So that the research team can search for the missing piece (piece C), please write the expression for the momentum of that piece in vector form.